In “aw yamūta karīm,” the speaker extracts a generous man from his own person and speaks of that figure in the third person.
In “lā khayla ʿindaka tuhdīhā,” the speaker addresses that same self as a different second-person addressee.
Both concern one actual person and an imagined counterpart, but the first uses an overt noun, “karīm,” while the second uses the mode of address.
Decisive point: Tajrīd need not be signaled by a special particle. Sometimes the structure of the utterance and its implied relationship between speaker and addressee is sufficient.